Big Idea:
To understand the concept of ratio and use ratio language to describe a ratio relationship between two quantities.

In order to assess prior understanding of a ratio, I’m going to ask the students to write down in their notes: what is a ratio? Why do we use ratios? What are some examples of real-world ratios? What do ratios mean?

This will give me a good idea of their understanding of ratios. Collect student ideas on a chart paper or the board. (this is just a collection of ideas and does not need to be corrected)

Begin by explaining to students that a ratio expresses the relationship between two quantities. Ratios compare two measures of same types of things (use an example from the classroom here: boys to girls, teacher to students) Allow time for students to come up with a few on their own. Next, have the students explain what that ratio means. I’m looking for them to say that for every 4 girls in class there are 5 boys as an example. Have students share their ratio and meaning with a partner. While students are sharing, be listening for them to use words like for every___ there are ___ or out of. Once students have had time to work with the language, begin discussing ratio relationships. I’ve included several examples to further extend the learning. Each problem will be asking students to make a statement about what it means. For example, if there are 3 drums for every students in band class, this would mean that many students would have to share a drum and not get as much playing time.

Ratios can be expressed as part to whole, part to part, or whole to part. Additionally, bring in the formats to writing ratios. (x:y, x/y, x to y) Developing this ratio relationship may be difficult for students, because they get confused by the order of the quantities. Showing students when quantities are written incorrectly will have different meanings. Also, it may be helpful if students begin labeling the quantities.

The students will be using their notes and manipulatives to see the different relationships. The notes will start them out with a scenario. They will have to then model the ratio (unifix cubes work well) and decide if it is a part to whole , part to part, or whole to part relationship and then write the ratio in its different formats. (SMP 2)

Resources (2)

Resources

Have students look over the chart that was made at the beginning of class. Ask students if there are any flawed pieces of information that can be removed from the chart based upon what they learned from class today? Next, ask them if they would like to add anything to the chart? And finally, ask them if there is anything on the chart they will stay, but could be tweaked a bit to make it more meaningful?

Use the following video as a teaching tool to reinforce student learning. It is interactive and will require students to come to the board/computer. It will be helpful to project this on to a larger screen so all students can participate.

When students are using the interactive piece, they will be stretched into looking at making equivalent ratios which is something we haven’t discussed yet. There are visuals on the screen to assist. When students are working on these, it will be important for them to remember that a ratio stays constant. So we always want the same ratio no matter what the quantities are. If students are really struggling with this, have them use their ratio table or unifix cubes to model it.

Erin Carr:
Responding to Michelle Schade
Thank you, that is what I thought, but I wanted to make sure I was telling my students the correct information. I appreciate your quick response! |
2 months ago |
Reply

Michelle Schade:
Responding to Erin Carr
There are a few ways to look at this. According to the standards, students need to be able to explain a ratio in words "For every _________ there are _________". Or they can also tell you that this is a part to whole, whole to part, part to part relationship. Additionally, for those students that are ready, they can start to look at a ratio and see other equivalent ratios or other ways to say it. For example... there are 2 boys and 3 girls in my family. I can also say there are 2 boys out of 5 people in my family. |
2 months ago |
Reply

Erin Carr:
Hi, this is a great lesson! My students definitely have a more in-depth understanding of what ratios are after teaching this, however, I am confused. What would you look for when explaining what the ratios mean? In the examples, what would they write if we were looking for the meaning of the ratios? |
2 months ago |
Reply

Thank you for the thoughtful lesson. A couple of suggestions: I would title #2 Developing AN Understanding of Ratios. And the last sentence of that sections is inaccurate. "For example, if there are 3 drums for every students in band class, this would mean that many students would have to share a drum and not get as much playing time." This is inaccurate. I assume "students" should really be "student," and the statement is exactly backward. Three drums for every student in the class means students have more drums than they need, not that they would need to share a drum.